A mathematical analysis of Prx2-STAT3 disulfide exchange rate constants for a bimolecular reaction mechanism

Free Radical Biology and Medicine 120 (2018) 239–245

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A mathematical analysis of Prx2-STAT3 disulfide exchange rate constants for a bimolecular reaction mechanism Troy F. Langford, William M. Deen, Hadley D. Sikes

T

⁎

Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge 02139, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Hydrogen peroxide Peroxiredoxin Thioredoxin STAT3 Rate coefficients Kinetic model

Appreciation of peroxiredoxins as the major regulators of H2O2 concentrations in human cells has led to a new understanding of redox signaling. In addition to their status as the primary reducers of H2O2 to water, the oxidized peroxiredoxin byproduct of this reaction has recently been shown capable of participation in H2O2mediated signaling pathways through disulfide exchange reactions with the transcription factor STAT3. The dynamics of peroxidase-transcription factor disulfide exchange reactions have not yet been considered in detail with respect to how these reactions fit into the larger network of competing reactions in human cells. In this study, we used a kinetic model of oxidation and reduction reactions related to H2O2 metabolism in the cytosol of human cells to study the dynamics of peroxiredoxin-2 mediated oxidation of the redox-regulated transcription factor STAT3. In combination with previously reported experimental data, the model was used to estimate the rate coefficient of a biomolecular reaction between Prx2 and STAT3 for two sets of assumptions that constitute lower and upper bound cases. Using these estimates, we calculated the relative rates of the reaction of oxidized peroxiredoxin-2 and STAT3 and other competing reactions in the cytosol. These calculations revealed that peroxiredoxin-2-mediated oxidation of STAT3 likely occurs at a much slower rate than competing reactions in the cytosol. This analysis suggests the existence of more complex mechanisms, potentially involving currently unknown protein-protein recognition partners, which facilitate disulfide exchange reactions between peroxiredoxin-2 and STAT3.

1. Introduction Elucidation of the molecular mechanisms through which hydrogen peroxide (H2O2) regulates cellular function remains a major challenge in the field of redox biology. Despite the widespread presence of oxidation-sensitive cysteine residues in proteins throughout cells [1–4], H2O2 reacts far too slowly with the vast majority of these proteins to compete with highly reactive antioxidant proteins that co-exist throughout the cell [5–7], such as glutathione peroxidases, peroxiredoxins, and catalase (which exists solely in the peroxisome) [8,9]. In recent years, a number of studies have suggested that peroxiredoxins consume essentially all of the H2O2 found in the cytosol on the basis of the combination of its high rate coefficient for reaction with H2O2 and its cytosolic abundance [5,10–13]. Thus, understanding the details of how oxidized peroxiredoxins may transmit these H2O2 signals to other proteins has emerged as an active line of inquiry. One hypothesis is that oxidized peroxiredoxins can oxidize secondary target proteins via a disulfide exchange reaction

[14–17]. In particular, Jarvis et al. demonstrated that human peroxiredoxin-1 (Prx1) can transiently oxidize ASK1 in response to a bolus addition of H2O2, and Sobotta et al. showed that human peroxiredoxin2 (Prx2) can oxidize the transcription factor STAT3 in human cells in order to inhibit gene transcription in response to stimulation with H2O2 [18,19]. In addition, Sobotta et al. demonstrated that oxidized STAT3 forms disulfide-linked dimers and tetramers upon oxidation by Prx2, and used non-reducing western blots to observe the dynamics of oxidized oligomer formation as a function of time in response to a bolus addition of H2O2. However, the oxidation-reduction steps and molecular mechanisms that control the dynamics of these processes are not completely understood. Kinetic models represent a powerful means to study the dynamics of these processes under specific conditions, as well as test hypotheses about different mechanisms that describe the same reaction pathway. By representation of reaction steps mathematically and comparison of predicted dynamics with experimental data from the same system under the same set of conditions, one can estimate unknown parameters

Abbreviations: H2O2, hydrogen peroxide; Prx, peroxiredoxin; Trx, thioredoxin; TrxR, thioredoxin reductase; STAT, signal transducer and activator of transcription; NADPH/NADP+, nicotinamide adenine dinucleotide; G6PD, glucose-6-phosphate dehydrogenase; EGFP, enhanced green fluorescent protein ⁎ Corresponding author. E-mail address: [email protected] (H.D. Sikes). https://doi.org/10.1016/j.freeradbiomed.2018.03.039 Received 25 October 2017; Received in revised form 9 March 2018; Accepted 20 March 2018 Available online 22 March 2018 0891-5849/ © 2018 Elsevier Inc. All rights reserved.

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Fig. 1. (a-b) Kinetic model used to simulate H2O2-mediated oxidation and reduction reactions in cytosol of human epithelial cells for model A (a) and model B (b). In model A, the disulfide form of Prx2 (Prx2SS) reacts with reduced STAT3, whereas in model B, the sulfenic acid form of Prx2 (Prx2SOH) reacts with reduced STAT3. Red arrows indicate the additional reactions that were added to create the expanded kinetic model. Red dashed arrows indicate key differences between model A and model B. Full kinetic model used in this study is shown in the Supplementary information.

reacted with STAT3, and one in which the sulfenic acid form (Prx2SOH) reacted with STAT3. These models will be referred to as model A and model B (Fig. 1a and Fig. 1b, respectively; full model shown in Supplementary Fig. 1a and Supplementary Fig. 1b). The initial concentrations of all species in the Prx2/STAT3 pathway, as well the rate coefficients for the associated reactions, are shown below (Table 1 and Table 2). All other initial species concentrations and rate coefficients were identical to those used by Lim et al. [12]. After construction of the expanded kinetic model, the system was simulated in response to 1.25 × 10–14 mol H2O2/cell (50 μM H2O2 bolus addition in a cell density of 4 × 106 cells/mL), and the concentrations of the species of interest were plotted as a function of time.

in the model consistent with the assumed mechanism. Currently, several mathematical models that describe the network of oxidation and reduction reactions involved in H2O2 metabolism inside human cells have been reported [8,9,12,13]. However, none of these models explicitly consider disulfide exchange reactions between “first-responder” antioxidant proteins such as Prx1 and Prx2 and other redox-regulated proteins. In this study, we modified a current kinetic model of H2O2mediated oxidation and reduction reactions in the cytosol of human epithelial cells to include reactions that describe Prx2-mediated STAT3 oxidation and reduction. We considered two cases to connect the data of Sobotta et al. to this model. First, we assumed that STAT3 oligomers formed rapidly after the initial reaction between STAT3 and oxidized Prx2. Thus, the number of oxidized STAT3 oligomers formed equaled the number of Prx2-STAT3 mixed disulfides formed at each point in time (i.e. Prx2-mediated STAT3 oxidation was the slowest step in this process and limited all subsequent reactions). We then used this model to determine the expected dynamics of Prx2-mediated oxidation of STAT3 in response to external H2O2 stimulation under these assumptions, as well as an estimate for the rate coefficient of STAT3 oxidation consistent with the model. Second, we assumed that oligomerization of STAT3 post-oxidation is the slower process and used a diffusion-limited value as an upper bound for the rate constant for reaction of oxidized Prx2 with reduced STAT3. Finally, we used the predictions from each set of assumptions to estimate the relative rates of Prx2-mediated oxidation of STAT3 compared to other reactions that competed for the oxidized Prx2 substrate in the system, as well as the implications of these rates for H2O2-mediated signal transduction in human cells.

2.2. Estimation of CSTAT3,

oxidized

and CSTAT3,reduced

In order to compare the predicted concentrations of oxidized STAT3 from the kinetic model, previously reported copy numbers per cell of STAT family members [27] in combination with experimental data reported by Sobotta et al. (Fig. 2b of [19]) were used to estimate concentrations of oxidized and reduced STAT3 in response to identical stimulation with H2O2 at various points in time. Sobotta et al. exposed HEK cells in suspension to bolus additions of H2O2 for various amounts of time, lysed the cells, and blotted the cell lysates for oxidized and reduced forms of STAT3. In order to estimate the relative amounts of oxidized STAT3 to reduced STAT3 after bolus addition of H2O2 from the experimental data, the intensities of both the oxidized and reduced bands were plotted as a function of position along the gel lane for each

2. Computational methods

Table 1 Initial concentrations of species in Prx-dependent H2O2 reduction pathway and STAT3 redox relay pathway simulated in kinetic model. Cellular density used in all simulations was 4.0 × 106 cells/mL.

2.1. Overview of kinetic model In order to predict the concentration of different species in the cell in response to a bolus addition of H2O2 over time, a kinetic model for H2O2 oxidation and reduction reactions in Jurkat cells originally developed by Adimora et al. [8], and later simplified and adapted to human epithelial cells by Lim et al. [12], was utilized. As a means to predict the concentrations of oxidized and reduced STAT3 in response to bolus addition of H2O2, the model was expanded to include reactions that describe H2O2 uptake from the extracellular media and Prx2mediated oxidation and reduction of STAT3. Currently, it is not known whether the sulfenic acid form or the disulfide-linked form of Prx2 reacts with STAT3 in the cytosol. For that reason, two expanded models were utilized: one in which the disulfide-linked form of Prx2 (Prx2-SS) 240

Species

Initial Concentration (M)

References

H2O2 (cytosol) Prx-SOH Prx-SS Prx-SH Oxidized Trx Reduced Trx NADPH NADP+ Oxidized STAT3 Reduced STAT3 H2O2 (media)

8.0 × 10–11 5.5 × 10−8 5.6 × 10–11 1.0 × 10−4 7.5 × 10−8 4.3 × 10−7 3.0 × 10−5 3.0 × 10−7 4.0 × 10−10 4.5 × 10−8 5.0 × 10−5

Lim et al. [12] Lim et al. [12] Lim et al. [12] Huang et al. [20] Adimora et al. [8] Adimora et al. [8] Martinovich et al. [21] Schafer and Buettner [22] Calculated Calculated Assigned

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Table 2 Rate coefficients used for key reaction expressions in Prx2-dependent H2O2 reduction pathway and Prx2-STAT3 redox relay pathway used in kinetic model. Note that kH2O2,perm in the table below is equal to the product of the cell permeability and cell surface area, divided by the volume of the cell (see Supplementary information for more details). Reaction Term

Rate Coefficient 7

k6([H2O2]Cyto)([Prx2-SH]) k9([Prx2-SOH]) k10([Prx2-SS])([TrxRed]) k19([TrxOx])([NADPH]) k20([NADPH])/(k5+ [NADPH]) k20([NADPH])/(k5+ [NADPH]) kH2O2,perm([H2O2]Med – [H2O2]Cyto) kSTAT3,ox([STAT3red])([Prx2-SH]) kSTAT3,red([STAT3ox])([Trx-SH])

Oxidized STAT3 (M) −10

0 10 20 30 45 60 90 120 150 180 240 300

4.0 × 10 2.2 × 10−9 4.2 × 10−9 6.4 × 10−9 7.4 × 10−9 9.5 × 10−9 1.2 × 10−9 1.2 × 10−8 1.1 × 10−8 1.1 × 10−8 1.0 × 10−8 5.5 × 10−9

−1

k6 = 1.3 × 10 M s k9 = 2.0 s−1 k10 = 2.1 × 106 M−1 s−1 k19 = 2.0 × 107 M−1 s−1 k5 = 5.7 × 10−5 M k20 = 3.8 × 10−4 M/s kH2O2,perm = 1.3 s−1 Fitted Fitted

Huang et al. [20] Huang et al. [20] Adimora et al., Low et al. [8,11] Arnér et al. [23] Yeh et al. [24] Yeh et al. [24] Calculated using [25,26] Calculated Calculated

time point i (Table 3). The rate coefficient for Trx-mediated reduction of oxidized STAT3 was fitted simultaneously with the same least squares minimization procedure.

Table 3 Concentrations of oxidized and reduced STAT3 in response to 1.25 × 10–14 mol H2O2/cell calculated from data reported in [19,27] using Eqns. S1-S3. Time (seconds)

References −1

Reduced STAT3 (M)

2.4. Sensitivity analysis of kinetic model

4.5 × 10−8 4.3 × 10−8 4.1 × 10−8 3.9 × 10−8 3.8 × 10−8 3.6 × 10−8 3.4 × 10−8 3.4 × 10−8 3.4 × 10−8 3.5 × 10−8 3.5 × 10−8 4.0 × 10−8

Sensitivity analyses were used to assess the robustness of each model's predictions. For example, the sensitivity of the predicted concentrations of oxidized STAT3 to various model parameters at a particular time point was defined by the following equation:

∂CSTAT 3 (t ) ki ∂ki CSTAT 3 (t ) C (k + Δki, t ) − CSTAT 3 (ki, t ) ki = STAT 3 i Δki CSTAT 3 (t )

si (t ) =

(2)

where CSTAT3 is the predicted concentration of oxidized species and ki is the model parameter that was varied during the simulation. The numerator of the sensitivity expression was normalized by the initial concentration of the species of interest, and the denominator was normalized by the initial value of the parameter that was modified. All parameters were perturbed by ten percent during this analysis, and sensitivity was evaluated at approximately 120 s after the start of the simulation (i.e. when the concentration of oxidized STAT3 was expected to peak). Absolute sensitivity was obtained from absolute value of the calculated sensitivity.

time point, and the total area under the curve for each oxidized STAT3 band was divided by the area under the curve for the reduced STAT3 band. Assuming that these bands accounted for all of the STAT3 in the cell, an expression for the concentration of the oxidized and reduced species at each point in time was obtained from the total cytosolic concentration of the STAT3 (calculated separately) as well as the ratio of oxidized to reduced species (Table 3; see Supplementary information Eqns. S1-S3 for more details). In order to estimate the total concentration of STAT3 in the cytosol, it was assumed that 5.0 × 104 copies of STAT3 were present in the cell. Reported copy numbers for STAT2 and STAT6 [27] were used to select this value, and the impact of other choices of copy number was examined and is presented in Supplementary Table 1. Cell volumes of 1.2 × 10–12 L (based on an average HEK293 radius of approximately 7.5 µm [25]) were used to calculate concentrations.

2.5. Calculation of the rate coefficient for STAT3 oxidation under diffusion control In order to calculate the theoretical upper bound for the rate coefficient of the reaction between free Prx2-SS and reduced STAT3 (i.e. the diffusion-limited rate coefficient), the following expression was used:

2.3. Determination of lower bound rate coefficients for STAT3 oxidation using predicted and calculated CSTAT3, oxidized,i

kD = 4πrAB DAB NAv

In order to estimate values for the rate coefficients for STAT3 oxidation in agreement with the model, the predicted concentrations were compared with calculated concentrations of the oxidized species under the same set of conditions. The square of the differences between the predicted and calculated concentrations of oxidized STAT3 were then computed at each point in time, and the rate coefficients for STAT3 oxidation and reduction were varied the MATLAB function FMINCON until the objective function below was minimized:

where kD is the diffusion-limited reaction rate coefficient, rAB is the sum of the radii of the two reactants, DAB is the relative diffusivity of the two reactants, and NAv is Avogadro's number. In order to estimate the radius of reduced STAT3, the radius of monomeric STAT3 was measured along the longest dimension in PyMol (PDB number: 3CWG). In order to estimate for the radius of Prx2-SS, it was assumed that the radius of Prx2SS is approximately double the radius of reduced monomeric Prx2. The radius of reduced monomeric Prx2 was then estimated along the longest dimension in PyMol (PDB number: 1QMV). The Stokes-Einstein relationship,

F=

∑ (CSTAT 3,predicted,i − CSTAT 3,calculated, i)2 i

Di = DEGFP 3 MWEGFP / MWi

(1)

where CSTAT3,predicted,i is the predicted concentration of oxidized STAT3 from the kinetic model at time point i, and CSTAT3,calculated,i is the calculated concentration of oxidized STAT3 from the experimental data at

(3)

(4)

was used to estimate the cytosolic diffusion coefficients of each protein, where Di represents the diffusion coefficient of either STAT3 or Prx2-SS, DEGFP represents the diffusion coefficient of EGFP, MWi represents the 241

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After estimates for the rate coefficients for STAT3 oxidation were obtained, a sensitivity analysis was performed on both of the expanded models to determine the rate coefficients that had the largest effect on the predicted concentration of oxidized STAT3 (Fig. 3a-b and Supplementary Fig. 2–6). Interestingly, neither the rate coefficient for the reaction between H2O2 and Prx2 nor the rate coefficient for the reaction between oxidized Trx and TrxR significantly affected the concentration of the oxidized STAT3 species in either model. Both of these reactions proceed with relatively high second order rate coefficients (on the order of 106–107 M−1 s−1), which likely results in low micromolar levels of oxidized Prx2 along with an abundance of reduced Trx (relative to the initial concentration) initially and suggests that neither oxidized Prx2 nor reduced Trx are limited in this system for a bolus addition of this magnitude at short times (i.e. within 30 s of H2O2 addition). As expected, the rate coefficient for Prx2-mediated oxidation of reduced Trx significantly perturbed the predicted concentration of the oxidized STAT3 species in model A, as both reduced Trx and STAT3 likely both compete for the same reaction partner (Prx2-SS). Similarly, the rate coefficient for Prx2-SOH sulfenic acid condensation significantly perturbed the predicted concentration of oxidized STAT3 in model B, likely due to the fact that STAT3 essentially “competes” with sulfenic acid condensation for oxidized substrate. Interestingly, in the first case, the predicted value of the rate coefficient for STAT3 oxidation consistent with the model was nearly four orders of magnitude lower than that of the reaction between Prx2-SS and reduced Trx, which is also believed to occur through a similar disulfide exchange mechanism [29]. This large disparity between the two rate coefficients, coupled with the relatively low concentration of most transcription factors in the cytosol (low to middle nanomolar range [27]) compared to cellular reductases such as Trx (middle to high nanomolar range [8,12] or higher [13]), suggests that reduced Trx should react with and reduce the majority of the oxidized Prx2 in the cytosol. Indeed, calculation of the relative rate of the two reactions revealed that Prx2-mediated STAT3 oxidation occurs nearly five orders of magnitude slower than Prx2-mediated Trx oxidation given the assumed rate coefficients and species concentrations (calculation shown in Supplementary materials). Similarly, calculation of the relative rate of Prx2-mediated STAT3 oxidation in model B compared to Prx2-SOH sulfenic acid condensation revealed that the former reaction also proceeds nearly five orders of magnitude slower than the competing reaction. In addition to the considerations above, Winterbourn et al. recently demonstrated that reduced glutathione is also able to react with oxidized Prx2 in both the disulfide and sulfenic acid form [30]. In both of these cases, glutathione acts as an additional competitor for oxidized Prx2 substrate in the

molecular weight of either STAT3 or Prx2-SS, and MWEGFP represents the molecular weight of EGFP. The diffusion coefficient of EGFP was obtained from a previously study that utilized fluorescence recovery after photobleaching to measure the amount of time required for cytosolic EGFP to migrate a fixed distance across a cell [28], and thus represents a realistic measure of how quickly this protein diffuses in an intracellular environment. The Stokes-Einstein relationship accounts for how differences in size impact the value of the diffusion coefficient, and has been used similarly in past work [12,16]. The relative diffusivity of the two reactants in all cases was equal to the sum of the calculated individual diffusivities. A list of all values used in the calculation of the diffusion-limited rate coefficient is shown in Table 4.

Table 4 Summary of values used in the estimation of the diffusionlimited reaction coefficient for the reaction between Prx2SS and reduced STAT3. Parameter

Estimated Value

rPrx2-SS rSTAT3,reduced DPrx2-SS DSTAT3, reduced

3.0 × 10−9 m 6.3 × 10−9 m 3.5 × 10–11 m2/s 2.8 × 10–11 m2/s

3. Results and discussion 3.1. Predicted lower bound for rate coefficient for STAT3 oxidation on the order of 102 M−1 s−1 In order to obtain a lower-bound estimate for the rate coefficient of Prx2-mediated STAT3 oxidation using the experimental data of Sobotta et al., we first assumed that the reaction between oxidized Prx2 and STAT3 occurs significantly slower than subsequent oligomerization steps. Under this set of assumptions, the rate coefficient for STAT3 oxidation was calculated using the values in Table 3 and the kinetic model. The calculated concentrations of oxidized STAT3 at each point in time and predicted concentrations that resulted from the least squares minimization procedure are shown (Fig. 2a-b). The values for the rate coefficients of STAT3 oxidation that produced the best fit with the experimental data were approximately 3.5 × 102 M−1 s−1 for model A and 8.3 × 102 M−1 s−1 for model B. With these rate coefficients in the kinetic model, the predicted concentration of oxidized STAT3 in response to 1.25 × 10–14 mol H2O2/cell reached a maximum concentration of approximately 12 nM at 120 s after stimulation with H2O2. Both model A and model B fit the experimental data equally well.

Fig. 2. Simulated STAT3 oxidation over time. (a-b) Predicted concentration of oxidized STAT3 at various time points (sold black line) with fitted rate constants for STAT3 oxidation and reduction in response to approximately 1.25 × 10–14 mol H2O2/cell for model A (a) and model B (b). The simulated oxidized STAT3 curve represents the best fit of the calculated concentrations (open blue circles) presented in Table 3. 242

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Fig. 3. (a-b) Absolute sensitivity of predicted concentration of oxidized STAT3 to various model rate coefficients at t = 120 s for model A (a) and model B (b) for a 10% increase in the rate coefficient of the indicated reaction. An absolute sensitivity of 1 indicates that for a 10% increase in a given rate coefficient, the predicted concentration of oxidized STAT3 increased by 10%.

Prx2 is the only species that oxidizes STAT3; while it is not clear whether other species can oxidize STAT3, Prx2 is the only species currently known to do so [19]. For that reason, interactions with other oxidized species were neglected. Second, it was assumed that Trx reacted with oxidized STAT3 to produce oxidized Trx and reduced STAT3; while it is not known exactly which species reduce oxidized STAT3 in human cells, it is well known that Trx serves as a general disulfide bond reductase in human cells [29,32,33], and it was previously shown that Trx forms a mixed disulfide intermediate with oxidized STAT3 [19]. For that reason, other types of STAT3 reduction pathways were not considered. Finally, it was assumed that these reactions followed mass action kinetics such that the rates of the reaction were equal to the product of the rate coefficient and the concentrations of the species in the reaction. It has been noted in the literature that STAT3 exists in a variety of conformations, oligomeric states, and subcellular localizations [19], in contrast with our treatment of reduced STAT3 as a homogenous pool of monomers. These complexities do not impact the predicted diffusion-limited rate constants, and thus do not change our central finding that only a very small amount of STAT3, if any, will react with oxidized Prx2 via a bimolecular mechanism. Conformational heterogeneity among STAT3 monomers would not be expected to impact the value of the cytosolic diffusivity, as different conformers would have similar size. Oligomers would diffuse more slowly than monomers, and thus, would compete even less effectively with Trx for reaction with oxidized Prx2. We estimated cytosolic STAT3 concentrations from per cell measurements [27], and thus other subcellular localizations could result in lower cytosolic concentrations. We used a sensitivity analysis to show that a 5-fold lower choice of STAT3 copy number per cell does not impact the predicted rate coefficient for the lower limit case (Supplementary Table 1). Concentration does not appear in the expression for the upper limit case (Eq. (3)). Another caveat of the results in this study is that several of the model parameters used to simulate this kinetic system were measured in only one type of cell. As a result, some model parameters could have different values in other types of cells. However, as shown in previous studies [6,8,12,13,16], non-Prx mediated H2O2 clearance pathways (black dashed box in Supplementary Fig. 1) do not significantly affect Prx-dependent H2O2 clearance pathways (red dashed box in Supplementary Fig. 1), and, among the reactions in this latter pathway, only variations in the rate coefficients for reactions in which oxidized Prx2 acted as a substrate affected the predicted concentration of oxidized STAT3 (additional sensitivity analysis of kinetic model shown in Supplementary Fig. 2–6). Similarly, variations in the initial

cytosol. Peskin et al. recently reported a value for the rate constant for the reaction between the sulfenic acid form of oxidized Prx2 and reduced glutathione of 500 M−1 s−1 [30]. Given this value, as well as the millimolar concentrations of reduced glutathione in the cytosol of most cells [12], this reaction should occur at a rate similar to that of sulfenic acid condensation (reaction 2 in Table 2), as well as nearly five orders of magnitude higher than the estimated reaction rate for the reaction between Prx2 and STAT3. 3.2. Predicted upper bound rate coefficient for STAT3 oxidation under diffusion control on the order of 5 × 106 M−1 s−1 In order to obtain an estimate of the theoretical upper bound for the rate coefficient for Prx2-mediated STAT3 oxidation, we next assumed that the reaction between oxidized Prx2 and STAT3 occurred so rapidly that only diffusion between the two species limited the formation of the reaction products. Under these conditions, the rate coefficient for the reaction is equal to the expression shown in Eq. (3). Given this expression, as well as the parameter values shown in Table 4, the diffusion controlled rate coefficient for this reaction was calculated to be approximately 4.6 × 106 M−1s−1. As expected, this value is lower than that of other well-known diffusion limited reactions [31], as both reactants are relatively large, bulky protein species that diffuse more slowly through the cytosol than small molecule species. Even under diffusion controlled conditions, the reaction between oxidized Prx2 and STAT3 proceeds nearly an order or magnitude slower than other reactions that compete for the same oxidized substrate (calculations provided as Supplementary information). This finding suggests that the direct reaction between oxidized Prx2 and STAT3 occurs at a kinetic disadvantage to other competing reactions in the cytosol. This conclusion could have important consequences for H2O2-mediated signaling cascades in cells, which are believed to occur at lower intracellular H2O2 concentrations than those used by Sobotta et al. (based on a H2O2 gradient across the plasma membrane of approximately 650-fold) [20]. If the reaction proceeds via a direct bimolecular reaction mechanism, Trx may reduce virtually all of the oxidized Prx2 produced from local H2O2 production under these conditions, and only a very small amount of STAT3, if any, will react with oxidized Prx2. 3.3. Caveats of the model and implications for H2O2-mediated signaling pathways in human cells The results obtained with this expanded kinetic model relied upon several assumptions that will be addressed here. First, it was assumed 243

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second set of assumptions, in which the reaction of oxidized Prx2 with STAT3 was assumed to occur very rapidly and at diffusion-limited rates in the cytosol, the estimated rate coefficient was determined to be approximately 4.6 × 106 M−1 s−1. Given these values, as well as estimates for the rate coefficients and concentrations of other species in the model, the relative rates of the different reaction pathways suggest that the reaction between oxidized Prx2 and STAT3 likely occurs at a kinetic disadvantage compared to other reactions in the cytosol that compete for the oxidized Prx2 substrate. Not only are the estimates reported here the first for this type of reaction, but they also offer insight into the kinetic competition that composes a central feature of these oxidationreduction reaction networks in cells, and allude to the existence of complex mechanisms for specificity in H2O2-mediated signaling reactions.

concentrations of virtually all of the species used in the model did not substantially affect the predicted concentration of oxidized STAT3 from the model, with the exception of reduced Trx. While variations in the initial concentration of reduced Trx did slightly perturb the predicted concentration of oxidized STAT3 (a 10% change in the reduced Trx concentration resulted in a 3% change in the predicted oxidized STAT3 concentration), variations in the initial concentration of reduced Trx did not significantly affect the relative rates of reaction extracted from the analysis (Supplementary Fig. 7–10 and Supplementary Tables 2–3). Several studies have suggested that peroxiredoxins act as a focal point of many redox signaling reaction pathways. Most recently, Travasso et al. demonstrated that peroxiredoxins exhibit attractive qualities as intracellular H2O2 signal transmitters due to the relatively high intracellular concentration of the sulfenic acid and disulfide forms of these proteins compared to intracellular concentration of H2O2 after extracellular H2O2 addition, and Antunes et al. demonstrated that Prx2 displays both the correct dynamic range and response time to act as a sensor and transmitter of H2O2 signals for extracellular H2O2 concentrations that result in STAT3 inhibition [15,16]. These studies did not address the question that our study addresses: once Prx2 is oxidized, how do the rates of reaction with STAT3 compare with those for reaction with Trx (model A) or conversion of Prx2SOH to Prx2SS (model B)? Our analysis suggests that the reaction between oxidized Prx2 and STAT3 likely occurs at a kinetic disadvantage compared to other reactions in the cytosol that compete for the same oxidized Prx2 substrate. One way that cells could achieve a higher rate of reaction between Prx2 and STAT3 is through a scaffold protein that acts as a tertiary species in the reaction and binds one or more of the reactant species. Recently, Bersweiler et al. [34] built upon the findings of Veal et al. [35] and demonstrated that the disulfide exchange reaction between the transcription factor Yap1 and the oxidized peroxidase enzyme Orp1 in yeast may proceed through a tertiary complex with the scaffold protein Ybp1 which binds both proteins and shields oxidized peroxidase from reduction. In light of similarities of this pathway and the STAT3-Prx2 pathway, it is possible that the reaction between STAT3 and oxidized Prx2 may also proceed through a similar mechanism. In complex with an adaptor protein, the rate constant of the reaction between the transcription factor and the oxidized peroxidase could increase, the rate constant of the reaction between the oxidized peroxidase and its reductase could decrease, or both. Currently, it is not known whether STAT3 requires the presence of an additional protein to react with oxidized Prx2. However, it is known that inactive STAT3 interacts with numerous proteins in the cytosol in response to various cytokines, and one of these proteins (later dubbed STAT3-interacting protein, or StIP1) was identified as a potential adaptor protein for STAT3 [36]. This protein, or closely related proteins, could serve as adaptor proteins for STAT3 and Prx2, and could merit additional research in the future. In addition to the reaction between Prx2 and STAT3 discussed in the preceding sections, it is also thought that Prxs can participate in redoxrelay reactions with several other redox-regulated proteins similar to the reaction between STAT3 and Prx2 [17]. These reactions may also require a third protein to facilitate the reaction between the oxidized and reduced species; it is currently unknown whether these other Prxmediated signaling reactions all utilize unique scaffold proteins (if any at all), but the details of these signaling processes remain an active topic of research.

Acknowledgements T.F.L acknowledges support from the Haas Family Fellowship in Chemical Engineering. H.D.S. acknowledges support from a Burroughs Wellcome Fund Career Award at the Scientific Interface and a Joseph R. Mares endowed professorship. Responsibilities were as follows: H.D.S, W.M.D, and T.F.L. conceived and designed the study, T.F.L. amended the code for the simulation, T.F.L. performed the simulations and related calculations, H.D.S., W.M.D, and T.F.L. interpreted the data, and T.F.L. wrote the manuscript with input from all authors. Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.freeradbiomed.2018.03. 039. References [1] N.K. Tonks, Protein tyrosine phosphatases: from genes, to function, to disease, Nat. Rev. Mol. Cell Biol. 7 (2006) 833–846, http://dx.doi.org/10.1038/nrm2039. [2] P. Chiarugi, F. Buricchi, Protein tyrosine phosphorylation and reversible oxidation: two cross-talking posttranslation modifications, Antioxid. Redox Signal. 9 (2007) 1–24, http://dx.doi.org/10.1089/ars.2007.9.1. [3] J. Ying, N. Clavreul, M. Sethuraman, T. Adachi, R. Cohen, Thiol oxidation in signaling and response to stress: detection and quantification of physiological and pathophysiological thiol modifications, Free Radic. Biol. Med. 43 (2007) 1099–1108, http://dx.doi.org/10.1016/j.freeradbiomed.2007.07.014. [4] P. Eaton, Protein thiol oxidation in health and disease: techniques for measuring disulfides and related modifications in complex protein mixtures, Free Radic. Biol. Med. 40 (2006) 1889–1899, http://dx.doi.org/10.1016/j.freeradbiomed.2005.12. 037. [5] C.C. Winterbourn, Reconciling the chemistry and biology of reactive oxygen species, Nat. Chem. Biol. 4 (2008) 278–286, http://dx.doi.org/10.1038/nchembio.85. [6] C.C. Winterbourn, M.B. Hampton, Thiol chemistry and specificity in redox signaling, Free Radic. Biol. Med. 45 (2008) 549–561, http://dx.doi.org/10.1016/j. freeradbiomed.2008.05.004. [7] L.E.S. Netto, F. Antunes, The roles of peroxiredoxin and thioredoxin in hydrogen peroxide sensing and in signal transduction, Mol. Cells 39 (2016) 65–71, http://dx. doi.org/10.14348/molcells.2016.2349. [8] N.J. Adimora, D.P. Jones, M.L. Kemp, A model of redox kinetics implicates the thiol proteome in cellular hydrogen peroxide responses, Antioxid. Redox Signal. 13 (2010) 731–743, http://dx.doi.org/10.1089/ars.2009.2968. [9] R. Benfeitas, G. Selvaggio, F. Antunes, P.M.B.M. Coelho, A. Salvador, Hydrogen peroxide metabolism and sensing in human erythrocytes: a validated kinetic model and reappraisal of the role of peroxiredoxin II, Free Radic. Biol. Med. 74 (2014) 35–49, http://dx.doi.org/10.1016/j.freeradbiomed.2014.06.007. [10] A.V. Peskin, F.M. Low, L.N. Paton, G.J. Maghzal, M.B. Hampton, C.C. Winterbourn, The high reactivity of peroxiredoxin 2 with H2O2 is not reflected in its reaction with other oxidants and thiol reagents, J. Biol. Chem. 282 (2007) 11885–11892, http:// dx.doi.org/10.1074/jbc.M700339200. [11] F.M. Low, M.B. Hampton, A.V. Peskin, C.C. Winterbourn, Peroxiredoxin 2 functions as a noncatalytic scavenger of low-level hydrogen peroxide in the erythrocyte, Blood 109 (2007) 2611–2617, http://dx.doi.org/10.1182/blood-2006-09-048728. [12] J.B. Lim, B.K. Huang, W.M. Deen, H.D. Sikes, Analysis of the lifetime and spatial localization of hydrogen peroxide generated in the cytosol using a reduced kinetic model, Free Radic. Biol. Med. 89 (2015) 47–53, http://dx.doi.org/10.1016/j. freeradbiomed.2015.07.009. [13] G. Selvaggio, P.M.B.M. Coelho, A. Salvador, Mapping the phenotypic repertoire of

4. Conclusions The purpose of the simulations described above were to analyze the dynamics of Prx2-mediated oxidation of the transcription factor STAT3. Under the first set of assumptions, in which reaction of oxidized Prx2 with STAT3 was assumed to be very slow compared to subsequent STAT3 oligomerization reactions, the rate coefficient for the former reaction was determined to be on the order of 102 M−1 s−1. Under the 244

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